Solve the equation 2 cos (x) + 1 = 0 2 cos x + 1 = 0, 0 ≤ x ≤ 2 π 0 ≤ x ≤ 2 π. Show all of your work

2π/3, 4π/3

Step-by-step explanation:

I interpret your question as asking us to solve the equation

2cos (x) + 1 = 0

2cos (x) = - 1

cos (x) = - ½x

x = arccos (-½), 0 ≤ x ≤2π

Since the cosine is negative, x must be in the second or third quadrant.

Referring to the unit circle, we find that

x = 2π/3 (120°) or x = 4π/3 (240°)